Given that
z₁ = 15 (cos(90°) + i sin(90°))
z₂ = 3 (cos(10°) + i sin(80°))
we get the quotient z₁/z₂ by dividing the moduli and subtracting the arguments:
z₁/z₂ = 15/3 (cos(90° - 10°) + i sin(90° - 10°))
z₁/z₂ = 5 (cos(80°) + i sin(80°))
so that z₁ is scaled by a factor of 1/3 and is rotated 10° clockwise.
Answer:
5
Step-by-step explanation:
-5 - (-10)
Here we have to use sign of multiplication rule.
negative * negative = positive
that is, -(-) = +
We use this rule and simplify.
- (-10) = + 10
Therefore, -5 + 10
When we have different sign of the numbers, we have to subtract from greatest to least number, then put the largest number sign in the answer.
-5 + 10 = + 5
Hence, the answer is 5
Hope this is will help you.
Thank you.
A. The ratio of lynx to mountain lions to wolverines is 2:3:1.
Thus, there are 2 lynx in the ratio. If there were 6 lynx, we would have to multiply all of the numbers in the ratio by 3 (because 6/2 = 3) to keep the ratio in the same proportion.
Therefore, because there is 1 wolverine in the ratio, and 1 * 3 = 3, if there were 6 lynx, there would be 3 wolverines.
b. We can use the same ideas that we had in part a to help us in part b.
There are 3 mountain lions in the ratio, but there are 15 mountain lions in the problem. Thus, the multiplier is 5, because 15/3=5.
Therefore, because there are 2 lynx in the ratio, and 2*5 = 10, if there were 15 mountain lions, there would be 10 lynx.
c. There is one wolverine in the ratio, but there are 10 wolverines in the problem. Thus, the multiplier is 10, because 10/1 = 10
Therefore, because there are 3 mountain lions in the ratio, and 3 * 10 = 30, if there were 10 wolverines in the park, then there would be 30 mountain lions.
d. The total number of lynx, mountain lions, and wolverines is 30.
To find out how many of each animal there should be, we must make an equation using the ratio and the variable x.
2x + 3x + 1x = 30
This equation means that the total number of animals together is 30, which is true. Now let's simplify by combining like terms.
6x = 30
Finally, we can simplify by dividing both sides by the coefficient of x, or 6.
x = 5
Thus, going back to our original equation, we know that the amount of lynx is 2x, mountain lions is 3x, and wolverines is 1x.
Lynx = 2x = 2(5) = 10 lynx
Mountain Lion = 3x = 3(5) = 15 mountain lions
Wolverines = 1x = 1(5) = 5 wolverines
Hope this helps! :)
Answer:
a. 1 1/2 (or 3/2)
b. 2/3
c. 1
d. 1
Step-by-step explanation:
Part A: (1,1) (7,5)
To determine the slope, you will use the equation m=(y2-y1)/(x2-x1). Keep in mind that it doesn't matter what point you use for (x1, y1) or (x2, y2).
Let's plug in the numbers for part a:
m=(7-1)/(5-1)
Let's then solve the problems inside the parentheses:
m=6/4
And finally, we simplify:
m=3/2 (or 1 1/2 depending on what your teacher wants for an answer)
For these others, I will just go through the steps and not explain them, if you need help or don't understand something I'm doing, either look back at what I did for part a or comment on this answer.
Part B: (1,1) (5,7)
m=(5-1)/(7-1)
m=(4/6)
m=2/3
Part C: (2,5) (-1,2)
m=(-1-2)/(2-5)
m=(-3/-3)
m=1
Part D: (2,5) (-7,-4)
m=(-7-2)/(-4-5)
m=(-9/-9)
m=1
